- Given that
$$\frac { 3 w + 7 } { 5 } = \frac { p - 4 \mathrm { i } } { 3 - \mathrm { i } } \quad \text { where } p \text { is a real constant }$$
- express \(w\) in the form \(a + b \mathrm { i }\), where \(a\) and \(b\) are real constants.
Give your answer in its simplest form in terms of \(p\).
Given that arg \(w = - \frac { \pi } { 2 }\)
- find the value of \(p\).
(ii) Given that
$$( z + 1 - 2 i ) ^ { * } = 4 i z$$
find \(z\), giving your answer in the form \(z = x + i y\), where \(x\) and \(y\) are real constants.
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